Cartesian vector application involving two forces.

[Failure007]

Homework Statement

Two forces act on an object at an angle of 50°. One force is 150 N. The resultant
force is 200 N. Find the second force and the angle that it makes with the
resultant.

Homework Equations

U_x=|U|cos(theta)
U_y=|U|sin(theta)

The Attempt at a Solution

Basically I began by trying to find the components of the 150 N force by using the formulas mentioned above, which left me with U = [150, 0]. I then tried adding the two forces together, i.e. R = [150 + v_x, 0 + v_y] and then tried to find the magnitude of the resultant, which I knew was equal to 200. I squared both sides leaving me with (150 + v_x)^2 + (0 + v_y)^2 = 40000, however I did not know where to go from here. Any help is appreciated, thanks a lot.

 

[Doc Al]

You haven't made use of the 50° angle. Assume that second force has a magnitude of F and makes an angle of 50° with respect to the x-axis. Use its components in the equation you wrote.

 

[Failure007]

If I'm understanding this correctly, could I assume that V_x=0.6428F and V_y=0.7660F and use those directly in my (150 + v_x)^2 + (0 + v_y)^2 = 40000 equation or would I have to use Fcos(50) and Fsin(50) instead? Thanks for the help so far.

 

[Doc Al]

Either way will work, as sin(50) = 0.7660 (at least to a good approximation). Personally, I would use cos(50) and sin(50), only plugging in values in the last step.

 

[Failure007]

Will do, Thanks a lot Doc Al.